United Kingdom

High-order quantum nonlinearity is an important prerequisite for the advanced quantum technology leading to universal quantum processing with large information capacity of continuous variables.
Levitated optomechanics, a field where motion of dielectric particles is driven by precisely controlled tweezer beams, is capable of attaining the required nonlinearity via engineered potential landscapes of mechanical motion.
Importantly, to achieve nonlinear quantum effects, the evolution caused by the free motion of mechanics and thermal decoherence have to be suppressed.
For this purpose, we devise a method of stroboscopic application of a highly nonlinear potential to a mechanical oscillator that leads to the motional quantum non-Gaussian states exhibiting nonclassical negative Wigner function and squeezing of a nonlinear combination of mechanical quadratures.
We test the method numerically by analysing highly instable cubic potential with relevant experimental parameters of the levitated optomechanics, prove its feasibility within reach, and propose an experimental test.
The method paves a road for unique experiments instantaneously transforming a ground state of mechanical oscillators to applicable nonclassical states by nonlinear optical force.


Bristol Quantum Information Technologies Workshop

Stroboscopic high-order nonlinearity for quantum optomechanics

quantum optomechanics

nonlinearity

quantum optics

quantum information

**BQIT is a three day annual workshop** aimed at enabling leading UK and international academics and industrial partners to come together; to explore and discuss future ambitions and challenges in the field of **Quantum Information Technologies.** Since our conception in 2014 we have had 230 speakers and panellists who have presented their work and opinions on a range of topics, from quantum theory to innovation in industry.


### Welcome Message
The BQIT:21 team welcomes you to the eighth Bristol Quantum Information Technologies workshop! 

Last year was the first time in our workshop's history that we had gone fully virtual. The global circumstances that continue to impact us all professionally and personally have forced BQIT once again to be delivered as an all-virtual workshop for 2021. The access this creates to colleagues across the world who would otherwise be unable to join us, as well as being able to make the workshop free for all attendees due to the lower costs involved in delivering an online workshop, are just a couple of the extraordinary benefits of meeting online. This also means that we can welcome three times as many attendees to BQIT than previous years.   

We take this opportunity to thank each of our speakers and poster presenters for contributing their technical content, this year's sponsors, whose support this year enabled BQIT:21 to be free to all attendees, and to all of our attendees for joining us online this year. We recognise the extra energy required to stay connected and motivated during these difficult times, and are hugely encouraged to see so many of you willing to continue to connect with us on an online platform. 

It is our hope that you have a productive and enjoyable time while you engage and interact with BQIT:21, and to everyone that has helped take BQIT:21 online, thank you! 

**The BQIT board and organisation team **


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### This year's workshop agenda is available here: [Virtual BQIT:21](https://drive.google.com/file/d/1QwsSM0ztnxC_lgUKf3TbO3GvnI44AQkY/view?usp=sharing)
For further information, please contact us at: **bqit-admin@bristol.ac.uk**

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poster

The discrete time crystal (DTC) is a recently discovered out-of-equilibrium phase of matter that spontaneously breaks discrete time-translation symmetry. Experimental observation has proven elusive due to the necessity of disorder-induced many-body localization to stabilize the DTC phase. Here, we observe the hallmark long-lived spatiotemporal order of the DTC phase using a quantum simulation platform based on individually controllable carbon-13 nuclear spins in diamond. The observed subharmonic response is robust for states with different temperatures, distinguishing the DTC phase from the prethermal subharmonic responses attributed to previous experiments. Our results provide the experimental signatures of a new out-of-equilibrium phase of matter and introduce a programmable spin-based quantum simulator for many-body physics.

Many-body-localised discrete time crystal in a programmable spin-based quantum simulator

The second law of thermodynamics allows one to associate the “forward” temporal direction to a positive variation of the total entropy produced in a thermodynamic process, and a negative variation with its “time-reversal” counterpart. Quantum physics admits also superpositions between forward and time-reversal processes, whereby the thermodynamic arrow of time becomes quantum-mechanically undefined. In this work, we demonstrate that a definite thermodynamic time’s arrow can be restored by a quantum measurement of entropy production. Furthermore, for small values (order of plus or minus one), the amplitudes of forward and time-reversal processes can interfere, giving rise to entropy-production distributions featuring a more or less reversible process than either of the two components individually, or any classical mixture thereof.

Quantum superposition of thermodynamic evolutions with opposing time's arrows

Masking of data is a method to protect information by shielding it from a third party, however keeping it usable for further usages like application development, building program extensions to name a few. Whereas it is possible for classical information encoded in composite quantum states to be completely masked from reduced sub-systems, it has to be checked if quantum information can also be masked when the future possibilities of a quantum computer are increasing day by day.
Newly proposed no-masking theorem [Phys. Rev. Lett. 120, 230501 (2018)], one of the no-go theorems, demands that except for some restricted sets of non-orthogonal states, it's impossible to mask arbitrary quantum states. Here, we explore the possibility of masking in the IBM quantum experience platform by designing the quantum circuits and running them on the 5-qubit quantum computer. We choose two particular states considering both the orthogonal and non-orthogonal basis
states and illustrate their masking through both the theoretical calculation as well as verication in the quantum computer. By quantum state tomography, it is concluded that the experimental results are collected with high fidelity and hence the possibility of masking is realized.

Masking of Quantum Information into Restricted Set of states

Quantum computation using a photonic platform requires fast switches to implement phase control in quantum processing circuits. Two common mechanisms for phase control in silicon photonics are thermo-optic and carrier depletion effects, each with their own advantages and drawbacks. The electro-optic Kerr effect provides an alternative phase-shifting mechanism in silicon that has been demonstrated using telecom wavelengths (Chakraborty, 2020). Here, we present devices with wider active-region waveguides to reduce insertion loss and have the added advantage of lower two-photon loss by using wavelengths in the mid-infrared (Rosenfeld, 2020). We demonstrate electro-optic phase shifts over a 60 nm band in the mid-infrared using devices with novel, wider waveguide geometries greater than or equal to 1 micron in width.

The Electro-Optic Kerr Effect in
the Mid-Infrared using Wide Silicon
Waveguides

This project explores Free Energy based Reinforcement Learning (FERL) with clamped Quantum Boltzmann Machines (QBM) applied to particle beam steering at the Super Proton Synchrotron at the European Centre for Nuclear Research (CERN). The objective is to study and push the performance of the FERL approach compared to classical RL techniques in terms of sample efficiency. The latter determines the number of interactions required with the environment during agent training and is a highly relevant figure of merit particularly for control of particle accelerator systems. FERL can provide a significant improvement of the learning efficiency as shown in earlier research. Training the QBM, however, requires sampling spin configurations from a Boltzmann distribution which can be efficiently achieved using quantum annealing hardware where the QBM is represented by the pairwise coupled qubits of the QPU. An FERL framework has been developed, including double Q learning and experience replay, as well as allowing for discrete and continuous state spaces. Results obtained from sampling spin configurations with quantum annealing, both simulated and employing D-Wave 2000Q hardware, are discussed and compared to the performance of classical deep Q learning.

Particle beam steering with quantum reinforcement learning

High-dimensional entanglement can give rise to stronger forms of nonlocal correlations compared to qubit systems. Beyond being of fundamental interest, this offers significant advantages for quantum information processing. The problem of certifying these stronger correlations, however, remains an important challenge. Here we theoretically formalise and experimentally demonstrate a notion of genuine high-dimensional quantum steering. We show that high-dimensional entanglement combined with judiciously chosen local measurements can lead to a stronger form of steering, provably impossible to obtain via entanglement in lower dimensions. Exploiting the connection between steering and incompatibility of quantum measurements, we derive two-setting inequalities for certifying the presence of genuine high-dimensional steering. We report the experimental violation of these inequalities using macro-pixel photon-pair entanglement certifying genuine high-dimensional steering in dimensions up to 15.

Genuine High-Dimensional Quantum Steering

Noise is ubiquitous in any realisation of a quantum computer and must be supressed using Quantum Error Correction (QEC). Recent works have shown that in the presence of biased noise significant improvements can be seen in the capabilities of error correcting codes. For continuous variable systems this bias can be artificially introduced through an appropriate choice of bosonic code. Here we study the code capacity behaviour of a biased GKP qubit concatenated with a simple n-qubit repetition code with the aim of drastically reducing the complexity of the error correction process. Preliminary findings indicate under a Gaussian displacement noise channel this code offers a performance improvement over a bare, square lattice GKP qubit.

Quantum Error Correction using Biased GKP States Concatenated with a Repetition Code

The integrated photon sources are part of the generation and manipulation of photons in photonic chips. In this work, we explore waveguides on Silicon Carbide as photon pair sources since it is scalable and manufacturable using lithography. This type of sources are tuned the geometry of these waveguides through the Spontaneous Four Wave Mixing process. We explore the co-propagating, co-polarized and monomodal propagation configuration. In the end, this work aims to be a compilation of physical characteristics of the waveguide and its corresponding spectral characteristics. It will also develop a workflow for the study of other materials such as Silicon Nitride (manufacturable with lithography) and Silicon Dioxide (manufacturable with direct femtosecond laser writing). We present the simulation and optimization of a waveguide in a spectral range related with availability of workplace devices (lasers and detectors).

DESIGN OF INTEGRATED PHOTON SOURCES FOR QUANTUM INFORMATION APPLICATIONS

The Hong-Ou-Mandel (HOM) effect is a fourth-degree interference originally intended to measure subpicosecond (or micrometre) time intervals between two photons. Lyons et al showed that there is sufficient precision in this method to measure the time delay with a HOM interferometer to the attosecond level (nanometre path length), giving a strong motivation to use this technique for thickness or refractive index estimation for transparent samples. Here, we propose a microscope using the HOM interference combined with a wavelength-entangled photon pair source allowing an interference fringe to be observed within the HOM interference dip. By varying the wavelength separation of the photons, the sensitivity of the microscope can be controlled. We propose to use temperature control of a periodically polled nonlinear crystal in a Sagnac architecture. By adaptively modifying the temperature of the nonlinear crystal in this arrangement, we aim to avoid ambiguity in parameter estimation.

The two-colour Hong-Ou-Mandel microscope

We study the interplay between entanglement and chaos in the time evolution of Bohmian trajectories of a two qubit system, made of coherent states of the quantum harmonic oscillator. This simple quantum system has very rich dynamics from a Bohmian standpoint, since with a proper choice of the physical parameters one finds ordered (periodic or non-periodic) and chaotic trajectories. We provide strong numerical evidence that the chaotic trajectories of this system are ergodic regardless of the amount of the entanglement and study their impact on the dynamical approximation to Born's rule for an arbitrary initial configuration of the quantum particles.

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